The burrs on the spine come from the past use of using a hammer on the back edge to aid driving the blade through something hefty, mine had one too, I ground off most of it then discovered using a hammer with these things makes them even more capable, hence why it was done in the past.
But modern use of sheet material should be fine if the sheet material contains some carbon and no doubt if sheet material was available in the past tool makers would have used it as the name of the game is produce a tool ata cost it will sell, minimise production and material costs and one can profit in small areas.
As mentioned earlier, I like my billhooks. Partly coz I use them as part of my daily work
The use of sheet material is as you say a cost saving device, but makers of old wouldn't have used it because their customers wouldn't let them. Billhooks made from a uniform thickness sheet just don't work as well, they flex in the wrong places, the weight is distributed in the wrong ways (usually, but different patterns effect this also) and the thickness of the blade behind the edge stops it penetrating well (which is also why I refuse to make scandi ground knives). The only reason they are selling hooks made this way today is because so few people use them and so those who care if a tool works proeperly or not can go and find an old billhook
Even the Morris hooks (made down the road from me) are only tapered in one direction (distal taper, not edge to back taper) these days as a way of saviing production costs; this mean that they work better than the pressed sheet metal ones but not as well as the old ones made in the same factory.
I make them, but they are a PITA to make properly so I don't make many. I could make them the way bulldog or even morris' do, but I want to make a tool that works as it should.